Non-perturbative aspects of Yang-Mills-Higgs theory
Yang-Mills-Higgs theory, being a part of the Standard Model, presents a great opportunity for investigation both from the point of view of theory and phenomenology. It contains regions in the theory’s parameter space which are suitable for Higgs like Physics and QCD like Physics. At the same time it presents a chance to study spectrum of the weak sector. For this purpose the choice of the SU(2) gauge group and scalar field in fundamental SU(2) are considered. The correlation functions are the key for investigation, because at least in principle knowing all the correlation functions gives us all the information about the theory under consideration. For the case of gauge dependent quantities, with the selection of minimal Landau gauge, propagators and three point vertices are considered for investigation in both regions of QCD like Physics and Higgs like Physics. It is found that even when scalar (Higgs) propagator and its vertices with the gauge fields are in agreement with what tree level perturbative calculations suggest, there is a considerable deviation in other propagators and other vertices. For the purpose of exploring spectrum in the theory, 0+ singlet and 1− triplet channels are considered. The decay from 0+ to 1− channel is also studied. There also exists a duality between single particle states and bound states, which is also studied in detail. For the Higgs which is discovered at LHC, the duality is found to exist while for heavier Higgs the existence of duality is no longer observed. Overall, the explored spectra suggest that Yang-Mills-Higgs theory may be a weakly interacting theory possibly till the time when Higgs mass is in TeV scale and the naive picture of a weakly interacting theory breaks down anyway and the theory becomes non-perturbative.